Chapter 8.2, Problem 12E

To determine

To graph:Graph the function. Compare the graph to the graph of $f(x)=x^2$.

Answer to Problem 12E

Graph:

  

Here, both the graphs are opened up and have the same axis of symmetry $x=0$ . The graph of $q$ is a vertical compression by a factor of $\frac{1}{2}$ units and a vertical shift by 6 units up of the graph of $f$.

Explanation of Solution

Giveninformation:

The function is $q(x)=\frac{1}{2}{x}^2+6$.

Graph:

To graph the function, let’s make the table values as follows:

$x$	$-2$	$-1$	0	1	2
$q(x)$	8	6.5	6	6.5	8

Now, plotting the ordered pairs and drawing a smooth curve through the points, we get the following graph.

  

Interpretation:

Here, both the graphs are opened upandhave the same axis of symmetry $x=0$ . The graph of $q$ is a vertical compression by a factor of $\frac{1}{2}$ units and a vertical shift by 6unitsup of the graph of $f$.